Sheet № 45 · Foundation + Higher · AQA · Edexcel · OCR
Perimeter –
Perimeter is one of the first geometry concepts you learn, but it still appears on every GCSE Maths paper — and the questions can be surprisingly tricky, especially when composite shapes or missing lengths are involved. AQA, Edexcel and OCR all test perimeter at both Foundation and Higher tiers, often combining it with algebra or circle c
§Key definitions
Step 1:
Work out any missing sides.
Step 2:
Add all outer sides: 14 + 5 + 9 + 4 + 5 + 9 = 46 m.
Step 3:
Total perimeter = 10 + 10 + 6 + 9.4248 = 35.4 cm (1 d.p.).
§Formulas to memorise
P = 2(l + w)
P = 4s
P = a + b + c
C = \pi d = 2\pi r
\text{Arc} = \frac{\theta}{360} \times \pi d
Rectangle:: $$P = 2(l + w)$$
Square:: $$P = 4s$$
Triangle:: $$P = a + b + c$$
Circumference of a circle:: $$C = \pi d = 2\pi r$$
Arc length (part of a circle):: $$\text{Arc} = \frac{\theta}{360} \times \pi d$$
Worked example
See example below.
An L-shaped garden has dimensions as shown: the overall length is 14 m, overall width is 9 m, and the cut-out rectangle is 5 m by 4 m. Find the perimeter.
⚠ Common mistakes
- ✗Forgetting a side. In composite shapes, students often miss one of the edges. Count the number of sides carefully.
- ✗Including internal edges. If two shapes are joined, the edge where they meet is not part of the perimeter.
- ✗Using πr² instead of πd for circumference. πr² gives area, not circumference. The circumference formula is C = πd or 2πr.
- ✗Not adding the straight edges of a sector. A sector's perimeter includes the arc and both radii.
- ✗Mixing up radius and diameter. If given the diameter, do not double it again.
✦ Exam tips
- →Label all the sides on the diagram, including missing ones you have calculated. This keeps your working clear.
- →For algebraic perimeters, set up the expression by adding all sides, then simplify. If the perimeter is given, set your expression equal to it and solve.
- →State the formula for circumference before substituting — this earns a method mark.
- →For semicircles in composite shapes, remember the perimeter includes the curved part only (the diameter edge is usually internal or already counted).
- →Double-check your answer by estimating. The perimeter of a shape should feel proportional to its size.